Jensen-Shannon divergence for compositional data

A composition carries only relative information, so it is closed to the simplex before the divergence is taken – which is exactly what Jsdiv(normalize = TRUE) does, and why the arithmetic is not duplicated here. Closure makes the answer invariant to the total. This is an information divergence on the closed parts, not an Aitchison distance: it is not subcompositionally invariant and uses no log-ratios. A zero part contributes zero, where a log-ratio geometry would be undefined – a reason to prefer it on sparse compositions and a reason not to call it Aitchison.

Usage

Compjsd(p, q, base = 2)

Arguments

p, q: Non-negative compositions over the same parts.
base: Logarithm base; 2 gives bits.

Value

As Jsdiv.

References

Lin (1991), IEEE Transactions on Information Theory 37:145-151; coded form from philentropy. See Jsdiv for the full note.

Examples

V <- c(1, 2, 3, 4, 5, 6, 7, 8)
Compjsd(V, V)
#> $estimate
#> [1] 0
#> 
#> $distance
#> [1] 0
#> 
#> $bound
#> [1] 1
#> 
#> $base
#> [1] 2
#> 
#> $n
#> [1] 8
#> 
#> $method
#> [1] "Jensen-Shannon divergence"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"